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<a href="#var-members">Variables</a> &#124;
<a href="#func-members">Functions</a>  </div>
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<div class="title">Cosine</div>  </div>
<div class="ingroups"><a class="el" href="group__group_fast_math.html">Fast Math Functions</a></div></div>
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<table class="memberdecls">
<tr><td colspan="2"><h2><a name="var-members"></a>
Variables</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">static const <a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__cos.html#gac597d7d00485bea7080b318b4473e83f">cosTable</a> [260]</td></tr>
<tr><td class="memItemLeft" align="right" valign="top">static const <a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__cos.html#ga012ad965e3493ffcc6dd7f9a12569e58">cosTableQ15</a> [259]</td></tr>
<tr><td class="memItemLeft" align="right" valign="top">static const <a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__cos.html#gafe999a5fcf1774a2292220071096b834">cosTableQ31</a> [259]</td></tr>
<tr><td colspan="2"><h2><a name="func-members"></a>
Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__cos.html#gace15287f9c64b9b4084d1c797d4c49d8">arm_cos_f32</a> (<a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> x)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">Fast approximation to the trigonometric cosine function for floating-point data.  <a href="#gace15287f9c64b9b4084d1c797d4c49d8"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__cos.html#gadfd60c24def501638c0d5db20f4c869b">arm_cos_q15</a> (<a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a> x)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">Fast approximation to the trigonometric cosine function for Q15 data.  <a href="#gadfd60c24def501638c0d5db20f4c869b"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__cos.html#gad80f121949ef885a77d83ab36e002567">arm_cos_q31</a> (<a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a> x)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">Fast approximation to the trigonometric cosine function for Q31 data.  <a href="#gad80f121949ef885a77d83ab36e002567"></a><br/></td></tr>
</table>
<hr/><a name="details" id="details"></a><h2>Description</h2>
<p>Computes the trigonometric cosine function using a combination of table lookup and cubic interpolation. There are separate functions for Q15, Q31, and floating-point data types. The input to the floating-point version is in radians while the fixed-point Q15 and Q31 have a scaled input with the range [0 +0.9999] mapping to [0 2*pi), Where range excludes 2*pi.</p>
<p>The implementation is based on table lookup using 256 values together with cubic interpolation. The steps used are:</p>
<ol type="1">
<li>Calculation of the nearest integer table index</li>
<li>Fetch the four table values a, b, c, and d</li>
<li>Compute the fractional portion (fract) of the table index.</li>
<li>Calculation of wa, wb, wc, wd</li>
<li>The final result equals <code>a*wa + b*wb + c*wc + d*wd</code></li>
</ol>
<p>where </p>
<pre>    
    a=Table[index-1];    
    b=Table[index+0];    
    c=Table[index+1];    
    d=Table[index+2];    
 </pre><p> and </p>
<pre>    
    wa=-(1/6)*fract.^3 + (1/2)*fract.^2 - (1/3)*fract;    
    wb=(1/2)*fract.^3 - fract.^2 - (1/2)*fract + 1;    
    wc=-(1/2)*fract.^3+(1/2)*fract.^2+fract;    
    wd=(1/6)*fract.^3 - (1/6)*fract;    
 </pre> <hr/><h2>Variable Documentation</h2>
<a class="anchor" id="gac597d7d00485bea7080b318b4473e83f"></a><!-- doxytag: member="arm_cos_f32.c::cosTable" ref="gac597d7d00485bea7080b318b4473e83f" args="[260]" -->
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          <td class="memname">const <a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> <a class="el" href="group__cos.html#gac597d7d00485bea7080b318b4473e83f">cosTable</a>[260]<code> [static]</code></td>
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<div class="memdoc">
<dl class="user"><dt><b></b></dt><dd><b>Example code for Generation of Cos Table:</b> tableSize = 256; <pre>for(n = -1; n &lt; (tableSize + 2); n++)    
 {    
	cosTable[n+1]= cos(2*pi*n/tableSize);    
 } </pre> where pi value is 3.14159265358979 </dd></dl>

<p>Referenced by <a class="el" href="group__cos.html#gace15287f9c64b9b4084d1c797d4c49d8">arm_cos_f32()</a>.</p>

</div>
</div>
<a class="anchor" id="ga012ad965e3493ffcc6dd7f9a12569e58"></a><!-- doxytag: member="arm_cos_q15.c::cosTableQ15" ref="ga012ad965e3493ffcc6dd7f9a12569e58" args="[259]" -->
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          <td class="memname">const <a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a> <a class="el" href="group__cos.html#ga012ad965e3493ffcc6dd7f9a12569e58">cosTableQ15</a>[259]<code> [static]</code></td>
        </tr>
      </table>
</div>
<div class="memdoc">
<dl class="user"><dt><b></b></dt><dd>Table Values are in Q15(1.15 Fixed point format) and generation is done in three steps </dd></dl>
<dl class="user"><dt><b></b></dt><dd>First Generate cos values in floating point: tableSize = 256; <pre>for(n = -1; n &lt; (tableSize + 1); n++)    
 {    
	cosTable[n+1]= cos(2*pi*n/tableSize);    
 }</pre> where pi value is 3.14159265358979 </dd></dl>
<dl class="user"><dt><b></b></dt><dd>Secondly Convert Floating point to Q15(Fixed point): (cosTable[i] * pow(2, 15)) </dd></dl>
<dl class="user"><dt><b></b></dt><dd>Finally Rounding to nearest integer is done cosTable[i] += (cosTable[i] &gt; 0 ? 0.5 :-0.5); </dd></dl>

<p>Referenced by <a class="el" href="group__cos.html#gadfd60c24def501638c0d5db20f4c869b">arm_cos_q15()</a>.</p>

</div>
</div>
<a class="anchor" id="gafe999a5fcf1774a2292220071096b834"></a><!-- doxytag: member="arm_cos_q31.c::cosTableQ31" ref="gafe999a5fcf1774a2292220071096b834" args="[259]" -->
<div class="memitem">
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        <tr>
          <td class="memname">const <a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a> <a class="el" href="group__cos.html#gafe999a5fcf1774a2292220071096b834">cosTableQ31</a>[259]<code> [static]</code></td>
        </tr>
      </table>
</div>
<div class="memdoc">
<dl class="user"><dt><b></b></dt><dd>Table Values are in Q31(1.31 Fixed point format) and generation is done in three steps First Generate cos values in floating point: tableSize = 256; <pre>for(n = -1; n &lt; (tableSize + 1); n++)    
 {    
	cosTable[n+1]= cos(2*pi*n/tableSize);    
 } </pre> where pi value is 3.14159265358979 </dd></dl>
<dl class="user"><dt><b></b></dt><dd>Secondly Convert Floating point to Q31(Fixed point): (cosTable[i] * pow(2, 31)) </dd></dl>
<dl class="user"><dt><b></b></dt><dd>Finally Rounding to nearest integer is done cosTable[i] += (cosTable[i] &gt; 0 ? 0.5 :-0.5); </dd></dl>

<p>Referenced by <a class="el" href="group__cos.html#gad80f121949ef885a77d83ab36e002567">arm_cos_q31()</a>.</p>

</div>
</div>
<hr/><h2>Function Documentation</h2>
<a class="anchor" id="gace15287f9c64b9b4084d1c797d4c49d8"></a><!-- doxytag: member="arm_cos_f32.c::arm_cos_f32" ref="gace15287f9c64b9b4084d1c797d4c49d8" args="(float32_t x)" -->
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          <td class="memname"><a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> arm_cos_f32 </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="arm__math_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a>&#160;</td>
          <td class="paramname"><em>x</em></td><td>)</td>
          <td></td>
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<div class="memdoc">
<dl><dt><b>Parameters:</b></dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">x</td><td>input value in radians. </td></tr>
  </table>
  </dd>
</dl>
<dl class="return"><dt><b>Returns:</b></dt><dd>cos(x). </dd></dl>
<dl><dt><b>Examples: </b></dt><dd><a class="el" href="arm_sin_cos_example_f32_8c-example.html#a11">arm_sin_cos_example_f32.c</a>.</dd>
</dl>
<p>References <a class="el" href="group__cos.html#gac597d7d00485bea7080b318b4473e83f">cosTable</a>, and <a class="el" href="arm__math_8h.html#a032503e76d6f69bc67e99e909c8125da">TABLE_SIZE</a>.</p>

<p>Referenced by <a class="el" href="arm__sin__cos__example__f32_8c.html#a52d2cba30e6946c95578be946ac12a65">main()</a>.</p>

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<a class="anchor" id="gadfd60c24def501638c0d5db20f4c869b"></a><!-- doxytag: member="arm_cos_q15.c::arm_cos_q15" ref="gadfd60c24def501638c0d5db20f4c869b" args="(q15_t x)" -->
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          <td class="memname"><a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a> arm_cos_q15 </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="arm__math_8h.html#ab5a8fb21a5b3b983d5f54f31614052ea">q15_t</a>&#160;</td>
          <td class="paramname"><em>x</em></td><td>)</td>
          <td></td>
        </tr>
      </table>
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<div class="memdoc">
<dl><dt><b>Parameters:</b></dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">x</td><td>Scaled input value in radians. </td></tr>
  </table>
  </dd>
</dl>
<dl class="return"><dt><b>Returns:</b></dt><dd>cos(x).</dd></dl>
<p>The Q15 input value is in the range [0 +0.9999] and is mapped to a radian value in the range [0 2*pi), Here range excludes 2*pi. </p>

<p>References <a class="el" href="group__cos.html#ga012ad965e3493ffcc6dd7f9a12569e58">cosTableQ15</a>, and <a class="el" href="arm__math_8h.html#a60b0142af7be007902142add27919b82">TABLE_SPACING_Q15</a>.</p>

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<a class="anchor" id="gad80f121949ef885a77d83ab36e002567"></a><!-- doxytag: member="arm_cos_q31.c::arm_cos_q31" ref="gad80f121949ef885a77d83ab36e002567" args="(q31_t x)" -->
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          <td class="memname"><a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a> arm_cos_q31 </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a>&#160;</td>
          <td class="paramname"><em>x</em></td><td>)</td>
          <td></td>
        </tr>
      </table>
</div>
<div class="memdoc">
<dl><dt><b>Parameters:</b></dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">x</td><td>Scaled input value in radians. </td></tr>
  </table>
  </dd>
</dl>
<dl class="return"><dt><b>Returns:</b></dt><dd>cos(x).</dd></dl>
<p>The Q31 input value is in the range [0 +0.9999] and is mapped to a radian value in the range [0 2*pi), Here range excludes 2*pi. </p>

<p>References <a class="el" href="group__cos.html#gafe999a5fcf1774a2292220071096b834">cosTableQ31</a>, and <a class="el" href="arm__math_8h.html#a8407c9e1347d10e3bcf0a7014f1fb2ff">TABLE_SPACING_Q31</a>.</p>

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